{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "# @author: tongzi\n",
    "# @created date: 2019/10/13\n",
    "# @description: principle component analysis\n",
    "# @last modification: 2019/10/13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽然 PCA 是一种非常基础的降维算法，但它仍然是一个非常有用的工具，\n",
    "尤其适用于数据可视化、噪音过滤、特征抽取和特征工程等领域。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.7391278364515688,\n",
       " 2.5801310701596343,\n",
       " -0.9477947579593763,\n",
       " 1.0195904306706842)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = (rng.rand(2, 2) @ rng.randn(2, 200)).T\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从图中可以看出， x 变量和 y 变量显然具有线性关系，这使我们回想起 5.6 节介绍的线性回归数据。但是这里的问题稍有不同：与回归分析中希望根据 x 值预测 y 值的思路不同，无监督学习希望探索 x 值和 y 值之间的**相关性**。  \n",
    "  \n",
    "在主成分分析中，一种量化两变量间关系的方法是在数据中找到一组主轴，并用这些主轴来描述数据集。利用 Scikit-Learn 的 PCA 评估器，可以进行如下计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.94446029, -0.32862557],\n",
       "       [-0.32862557,  0.94446029]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 成分\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7625315, 0.0184779])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 解释方差\n",
    "pca.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了查看这些数字的含义，在数据图上将这些指标以向量形式画出来，用“成分”定义向量的方向，将“可解释差异”作为向量的平方长度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops = dict(arrowstyle='->', linewidth=2,\n",
    "                     shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.7391278364515688,\n",
       " 2.5801310701596343,\n",
       " -0.9477947579593763,\n",
       " 1.0195904306706842)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.3)\n",
    "for vector, length in zip(pca.components_, pca.explained_variance_):\n",
    "    v = -vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这些向量表示数据主轴，上图的箭头长度表示输入数据中各个轴的“重要程度”——更准确地说，它衡量了数据投影到主轴上的方差的大小。每个数据点在主轴上的投影就是数据的“主成分”。  \n",
    "这种从数据的坐标轴变换到主轴的变换是一个仿射变换，仿射变换包含平移（translation）、旋转（rotation）和均匀缩放（uniform scaling）三个步骤。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1.用PCA降维  \n",
    "用 PCA 降维意味着去除一个或多个最小主成分，从而得到一个更低维度且保留最大数据方差的数据投影。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_pca=  pca.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original shape: (200, 2)\n",
      "transformed shape: (200, 1)\n"
     ]
    }
   ],
   "source": [
    "print(f\"original shape: {X.shape}\")\n",
    "print(f'transformed shape: {X_pca.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "变换的数据被投影到一个单一维度。为了理解降维的效果，我们来进行数据降维的逆变换，并且与原始数据一起画出:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.77152878069022, 2.661757596590677, -0.9964674432667127, 1.0219081775900811)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = pca.inverse_transform(X_pca)\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浅色的点是原始数据，深色的点是投影的版本。我们可以很清楚地看到 PCA 降维的含义：沿着最不重要的主轴的信息都被去除了，仅留下了含有最高方差值的数据成分。被去除的那一小部分方差值（与主轴上分布的点成比例，如上图所示）基本可以看成是数据在降维后损失的“信息”量。  \n",
    "  \n",
    "  \n",
    "这种降维后的数据集在某种程度上足以体现数据中最主要的关系：虽然有 50% 的数据维度被削减，但数据的总体关系仍然被大致保留了下来。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.用PCA作数据可视化  \n",
    "降维的有用之处在数据仅有两个维度时可能不是很明显，但是当数据维度很高时，它的价值就有所体现了。为了证明这一点，来介绍一个将 PCA 用于手写数字数据的应用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "该数据包含 8 像素 ×8 像素的图像，也就是说它是 64 维的。为了获得这些\n",
    "数据点间关系的直观感受，使用 PCA 将这些数据投影到一个可操作的维度，比如说二维：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "projected_data = pca.fit_transform(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
    }
   ],
   "source": [
    "print(digits.data.shape)\n",
    "print(projected_data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "画出每个点的前两个主成分，更好地了解数据:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2a118818d30>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(projected_data[:, 0], projected_data[:, 1], \n",
    "           c=digits.target, alpha=0.5, \n",
    "            cmap=plt.cm.get_cmap('viridis', 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们已经介绍过这些成分的含义：整个数据是一个 64 维的点云，而且这些点还是每个数据点沿着最大方差方向的投影。我们找到了在 64 维空间中最优的延伸和旋转方案，使得我们可以看到这些点在二维平面的布局。上述工作都是以无监督的方式进行的，即没有参考标签。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3.成分的含义"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以进一步提出问题：削减的维度有什么含义？可以从基向量的组合角度来理解这个问题。例如，训练集中的每幅图像都是由一组 64 像素值的集合定义的，将称其为向量$x$:  \n",
    "$$ x = [x_1, x_2, x_3,.., x_{64}] $$  \n",
    "我们可以用像素的概念来理解。也就是说，为了构建一幅图像，将向量的每个元素与对应描述的像素（单位列向量）相乘，然后将这些结果加和就是这副图像：  \n",
    "$$ image(x) = x1 * pixel_1 + x2 * pixel_2 + ... + x_{64} * pixel_{64} $$  \n",
    "我们可以将数据的降维理解为删除绝大部分元素，仅保留少量元素的基向量（basisvector）。例如，如果仅使用前 8 个像素，我们会得到数据的 8 维投影（如图 5-85 所示）。但是它并不能反映整幅图像，因为我们丢掉了几乎 90% 的像素信息。  \n",
    "![image.png](attachment:image.png)  \n",
    "面板的上面一行是单独的像素信息，下面一行是这些像素值的累加，累加值最终构成这幅图像。如果仅使用 8 个像素成分，就仅能构建这个 64 像素图像的一小部分。只有使用该序列和全部的 64 像素，才能恢复原始图像。  \n",
    "  \n",
    "但是逐像素表示方法并不是选择基向量的唯一方式。我们也可以使用其他基函数，这些基函数包含预定义的每个像素的贡献，如下所示：  \n",
    "$$ image(x) = mean + basis_1 * pixel_1 + basis_2 * pixel_2 + ... $$  \n",
    "PCA 可以被认为是选择最优基函数的过程，这样将这些基函数中前几个加起来就足以重构数据集中的大部分元素。用低维形式表现数据的主成分，其实就是与序列每一个元素相乘的系数。图 5-86 是用均值加上前 8 个 PCA 基函数重构数字的效果:  \n",
    "![image.png](attachment:image.png)  \n",
    "  \n",
    "与像素基不同，PCA基可以通过为一个均值加上8个成分，来恢复输入图像最显著的特征。每个成分中像素的数量必然是二维数据示例中向量的方向。这就是 PCA 提供数据的低维表示的原理：它发现一组比原始的像素基向量更能有效表示输入数据的基函数."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 4。选择成分的数量  \n",
    "在实际使用 PCA 的过程中，正确估计用于描述数据的成分的数量是非常重要的环节。我们可以将累计方差贡献率看作是关于成分数量的函数，从而确定所需成分的数量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'cumulative sum of expained variance')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(digits.data)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative sum of expained variance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由图可知，二维的投影会损失很多信息（正如解释方差所表示的）。我们需要大约 20 个成分来保持 90% 的方差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 5.9.2用PCA过滤噪声  \n",
    "PCA 也可以被用作噪音数据的过滤方法——任何成分的方差都远大于噪音的方差，所以相比于噪音，成分应该相对不受影响。因此，如果你仅用主成份的最大子集重构该数据，那么应该可以实现选择性保留信号并且丢弃噪音。  \n",
    "画出几个无噪音的输入数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                            subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                            gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8), cmap='binary', \n",
    "                  interpolation='nearest', clim=(0, 16))\n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在添加噪声："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(42)\n",
    "noisy = rng.normal(digits.data, 4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c0YI/1ActaBYRKVKkiKqjcSLi9TILeK3mpy1WtRakomPhXKfSpUv77hOCyOB/+x2f8fHxqh4Vpd/uVt7ovf36kQWgXkPNv87yuUHnHOwb9+83McaDNX7DQM3vV3xe2QixsFalTJkyqm75TYXAM0b9ghYch/LB80Nuj1G/BHv8ZRHOcwYt+g/zGuZKfnFxcXrwMJ6vofwrw8BzElY1ViMRwS6deZPGIrIs4LVrOTK/vE9gjq7nJ+Jejq7nJ8IxmtdxPT8Rb47mZCe/iNQVkVQR8dqC5y0iRaSUiKwSkcC6OFdyZH55Oz8RPUfX8xNxJ0fX8xPhGM3rObqenwjO0ZzsEEIIIYTkebhAmRBCCCFOYy1Q/r/w05YrOTK/vJ2fCP9EkNdzdD0/EY7RvJ6j6/mJGH/GsiY7dcX9RUuu5cj88j6BObqen4h7ObqenwjHaF7H9fxElAXK1mQnFR149913YaeePXuq+ubNm1W9f//+MFaDBg1UHflv5YDgnGCOu3fvhkGQl9D06dNVHZVfi4gMHjxY1X/44QfYxyh3znF+U6dOhfEzMjJUPSUlRdUffPBBGAt5Oln+SZUqVUKHcpyfxR//+EdVnzZtmu9YU6ZMUfWDBw/CPr1797ZCpoJ/ZyMzMxMGWLZsmaqjUu6+ffvCWHv37lV1a63f/PnzPVpsbKw0adJEBFzDvXv3yqVLl7IdQD5JIvj+3LRpk6qjsnsRkV9++UXVUe4i3vunQIECWfeBmt/HH38s6enp2Q60bNkSxkdly+jZN2nSJBjLyiNMcjRGLc6fP6/qb775pqr/5S9/gbGQt5n13XLjjTcaZ5c7zxnktXfvvfeqOtrSRERkzpw5qj5r1izYp169euhQjvM7c+YMjH/06FFVR55c1jhEPmYnT56EfbQtR/Lly5e1rYEnJ2uyA3/OOnv2rNFNBz1Q0BeoiG1uFybBOcEcgx+8OQEZZVp7ISDTxmDTwByS4/zQuYrgBxG6Hsj4TQRPdsL5fMVHfhboxkLXwgJ9VuHcI9e4DP6dDWuygSaraLITTt4W6DO5hnoNL1265HlGHD9+HAZJTdWfzyiXcCY7Fsb9o+aXnp7uGRPh3OOnT59W9dy+hiHI0Ri1QOMXfbla+aFxEs51vUauPGfQOaNJQmJiou9Y1rPXIMf5XblyBQZBn284YxG9j3UNQ9w/noNcoEwIIYQQp+FkhxBCCCFOw8kOIYQQQpzGWrMD+d3vfgePWX42GuPHj4fH0GJD6z3QWhC/nivW308R27dvV/UnnnjCdyzkHZNbDB061Pd7o7+NV6hQAcZ69tlnVf3w4cOwz7Zt27K9joqKshYtq7z++uvwGPJhefjhh1Xd+rs1Whz52GOPwT59+vTxaEWKFIGLT8+dO+dZ44D8r0RE2rRpo+rovrF8adAiT7QwW0SkadOmOX7vLCpXruzR2rdvD9t36tRJ1e+44w5Vt7zY3n77bfPcNKz7R+O+++7zrDFA629EsJ/VSy+9pOqPP/64r/MRsdftrVq1yqPFxsbCz1dbW2F5ummLS8Plv/7rv1Tduq633HJLrry39bn/+OOPqo7uBWNBMcRPIUtUVBRcNI2wvNh69eql6miNKirsERFp166dqlsL0/3CX3YIIYQQ4jSc7BBCCCHEaTjZIYQQQojTcLJDCCGEEKfhZIcQQgghTsPJDiGEEEKcJqzSc6uMEzFw4EBVt0r3JkyYoOpWKbffEnORq/YBweXFpUqV8h3H8qdB3HfffaqeP39+2Cd4u/F8+fKZXlP79u3zlORb3l+oxHz9+vWq/uSTT8JYqPTc2uo7uGTS73YGIiKDBg3y3Qd5Sv35z3/2HcuyCLE8nzQuX77sKT1HPmwietmwheV11717d1W3xueLL77o0cK5hh07doTH0DVBJfHW5/UrbAVyzNdff+2xi7DGKNqGAH2ONWrUgLFQCXTBggVhH237AIvly5d7/NqQt6GISP369WEcDVRyLyJSrVo1VbcsVTQ7l4iICLMkfvfu3Z7naI8ePWB7VBaOfK4sj0E0RkeMGAH75AbdunWDx9C2FHPnzlX1PXv2wFioxHznzp2wz7fffuvREhMT4TOLv+wQQgghxGk42SGEEEKI03CyQwghhBCn4WSHEEIIIU7DyQ4hhBBCnCasaiyr0iQ5OVnVz58/7/t9PvzwQ1XPyMjwHcvCMjvT6NChg6ojg9SlS5fCWL1791b1xYsXwz7BppihKtCSk5M91WaWseb777+v6sFVYFns2rULxtq4caOq33zzzbBPbrB//354rGzZsqr+hz/8QdWPHTsGY6GKj2nTpsE+WuVBUlISfP/169d7Kl1uv/12GL9fv36qrlUviIikpqbCWD179lR1y7QwPT3do0VGRkpCQgLso2FVlY0aNcpXLKuCc+3ataquVexk4dcouECBAp5KqpkzZ8L26FmCxluVKlVgrBtuuEHV0bM6HBITEz0VeidPnoTtUfXN5MmTVX3kyJEwlmasK4KfPSIiR44c8WiW0amIbWSpge7Rr7/+WtWtqsC7775b1S0j0IYNGxpnlzM++OAD333GjBmj6tpnnsVbb72l6shsVERkwIABvs6Lv+wQQgghxGk42SGEEEKI03CyQwghhBCn4WSHEEIIIU7DyQ4hhBBCnCasaixrlX3Lli1V3a8fkIjI5s2bVb1u3bqwj+Y7Eh8fL82bN4d90tLSPNVK77zzDmw/e/ZseExj2LBh8FixYsVUHVVjiNieLxrbt2+XCxcuZNMaNWoE2992222qXrVqVVW/ePEijFW9enVVT0tLg33C8V4LBlVcieDxizyirMon5FXk9xpZpKSkeCqcvvnmG9geVY00a9ZM1ZF/mQiumjt9+jTsU7JkSXjMD9Z9vnfvXlVft26dqrdt2xbG2rp1q6rfeOONsE+wZ09UVJSUL18ettcqOL/44gvYHlVElihRQtXvvPNOGOvQoUOq/vTTT8M+qCoKcfbsWU/FoFXF2KZNG1VH3x8WqJrQ8prasGGD7/fRQH56IiILFixQ9eDPKYvOnTvDWH379lV169nrl7Nnz3qeW9azGF3fVq1aqbp1PyMftQMHDsA+o0ePhsc0+MsOIYQQQpyGkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0nOwQQgghxGk42SGEEEKI04QsPd+yZYvHoOyWW26B7ZcvX67qyOhr8ODBMFbhwoVVferUqbCPVf6JOHPmjFy6dCmb9vjjj8P2qAzw+PHjqm6VvWumiSJ26Tkqd0acOnXKlxErKjH/7rvvVP3gwYMwFsrvp59+gn2Q6V1ugcbV22+/repWGTm6Fpb5q1Z2HxcXJ02bNlXbd+3a1aN9//33MH5wWXQWKO9NmzbBWNpWDiJ4W4hw+fzzz+XcuXPZtOuvvx62R6WqwVss5ARUxm6V1webB/u9J0VEWrduDY+h7S2QmeK4ceNgrKFDh6r6ihUrYB/NSDcyMlLKlCmjtteeVzt27IDxH330UVW3tlRAoK0OJk6cCPto90/+/PnNbSY0kMmqCDYj7tSpk6pb3zloawG0dYmI996Nj4+HJf8iV8dcsPlt+/btYfvSpUv7OifLMBqN0bFjx8I+LD0nhBBCCAmAkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0nOwQQgghxGlCVmNFRER4Kg1SUlJg+3r16qn6kCFDVN1aTY5M74Krw34tWtUHqjwSEVg1U6lSJVVHFRQiIidOnFB1q5Jg48aN2V5HR0dLtWrVYPt69ep5jE5//PFH2B6ZoE6aNEnVa9WqBWMhU0rLJDAjIyPb64iICMmfPz9sP3ToUE8l3IwZM2D7tWvX+tKjo6NhLMS8efPgsRdeeMFXrH/84x+eCq7hw4fD9o0bN/YVP18+/H+edu3aqbplknn06FH1PYoWLQr7FClSRBISErJpllltjx49VP3DDz+EfRDIfHL8+PGwT3BFZqhqrOBqT5Gr5qGImjVrqnqTJk1U/d5774WxUJWPNa6150N8fDysxvruu+88961VbYbOCVXzWhWaKHerMler4Ap1DS9cuOCpzLTG9Ny5c3P83iJ29VqFChVU3bp3u3TpAo9pdO7c2ZNffHw8bI8MTdE5FSlSBMZ64403VN0ybJ0/f75Hi42NhZXM/GWHEEIIIU7DyQ4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUKWnhcvXtxTtmyV26GSUNTnn//8J4zVsWNHVa9SpQrsk1tYZa89e/ZU9T179qi6Vb5XqlQpVQ82ZAtkwYIF2V4nJSWZpecFCxb0aFaZI+KJJ55QdasMGZUCIzM8kauGg34YNGiQp7R3ypQpsP2TTz6p6miMamXDWaDyXcssd8uWLWqcypUrq+0HDBjg0d577z0YH92DaKxZRqfICBCZjYpcLf8MJtQ1veOOOzwaup9EsIll8LMqi4ULF5rvr2GZFD/99NPZXhcqVEhGjBgB21tl5n7ee9SoUapeo0YNX/FFrj43EJp5sVWajbbjQCCz4WeeeUbV0ZgWsbcJQWhjNBTa9hfW9gTIAPqvf/2rqi9ZsgTGQuMdGeKKiHz22WfZXsfFxZlbFMTFxcFjGq1atVL1RYsW+YojcnWeoRHOlgMI/rJDCCGEEKfhZIcQQgghTsPJDiGEEEKchpMdQgghhDiNtWouUsT23tBAi5wKFy6s6pbPlbWALkyCV0n6Wwl7DbSQFS3gK1euHIxVunRpX7FEvJ9LgQIFsv6Z4/yCfYgCQdcK+VMFvL8H5G+WmJgI+xio+WmLP61zKlu2rKqjvC3QAmXr89X6BOQQmGNY1w9x3XXXqbrlO4bex1pwqy1GDtByPEat90AeTeh5Es6CVItChQplex1QBJArzxgEGrvnz5/3Hcu6B7XnT4CWozEaDqiYA+X9G5Hja2h9hugZhBbjWuPdukcRwd/FAfdAroxR9Gy3vu8Q6DsVvUcO8OQUYVRiNBKR78N9p/9QGovIsoDXruXI/PI+gTm6np+Iezm6np8Ix2hex/X8RLw5mpOd/CJSV0RSReTyb3tevzmRIlJKRFaJyIUA3ZUcmV/ezk9Ez9H1/ETcydH1/EQ4RvN6jq7nJ4JzNCc7hBBCCCF5Hi5QJoQQQojTWAuU/y/8tOVKjswvb+cnwj8R5PUcXc9PhGM0r+foen4ixp+xrMlOXXF/0ZJrOTK/vE9gjq7nJ+Jejq7nJ8IxmtdxPT8RZYGyNdlJFRG5cOGC54BVBjd79mxVR35ESBcR6dKli6pb5WgpKSkeLTIyMssXKDXoUKqIyLp16+TixYvZDtStWxe+B2LOnDmqbvnyLF68WNU3bNjg+/0F5OeXZs2aqTryQxozZgw+oVT9FEaOHAn7rFq1KtvrmJgYqVmzpoiP/NLS0mD8lStXqjryNrK2ATh9+rSqb9y4EfYJUUaaGvzv1NRUuXw5+3+4UBl5ODz44IPw2A033KDqFStWhH2Qd9w1cnwN586dC4Mgr6C77rpL1U+ePAljIW83y4Mv2NMvISFB2rVrJwLyW7x4sWRkZGQ70LJlSxgf0b9/f1WfP38+7POPf/xD1Vu0aOH7/a/hGaMnTpzw+JKh7wIRkYcffljVkecbykFEJDk5WdUfffRR2CfEZ5/jMWp5DL722muqjsabdU7I+3DZsmWqLqL7zV17lqn5LViwwDNG77//fhgffXej5+vAgQNhLOQlaD17q1evDo+Jcs2syc6/n65+FjGfO3dO1fft26fqZ86cwSdw2f8vapZpo3h/orssInLx4kV1UucXlPuxY8dgn/379//q9w1Azc8vhw4dUnV0DS3T0lOnTvl+f+Na5Dg/ZAgpIp4bOosDBw6ounXDWV+iYXI5+N+XL18ONa5/FUeOHIHH0J4gxYoVC/ftcnwNrb1j0OeOrm16ejqMFfwfnZxgxFPzy8jICGsvnGDQswTdmyLh7cETAs8YvXLliuees/7DgUDPkoMHD8I+6Jr/irxzPEatfeLQtUJ7q1mxEJmZmb77iDFG0XeYxvHjx1Vd+8FBJLx70Hr2hsBzzbhAmRBCCCFOw8kOIYQQQpzG2menvIjs8Ruwfv36qo7+xh4O27dvh8esv7OLSAUR2RvwuryI7NoTTPcAABm5SURBVNm/f7/nzwTWT7C1atUKfZIBWOsb9uzRP2LrT4fBPzVGRERkbbOu5qf9OdD68xk632vrZjysW7cOxlqwYIGqo3VBIVDz27Jli+cnYPTnFxHJWr/lYfLkyaq+detWGGvChAmqPnHiRNinX79+8Jhkz7G8gHvQun5oa/1x48ap+lNPPQVjzZgxQ9Ufeugh2CcE6jU8efKk588g1k/qtWvXVvUOHTqourX+59lnn1X1QYMGwT516tTJ9rpUqVLyxRdfiID8YCAAGqPoz5noTwoiIqNHj1b1u+++G/Zp0qSJcXY5G6MWaK3J448/rurWGkp0bW+99VbY55FHHvFocXFxWWu+1Gs4ceJEz7ILa+3hX/7yF1VHfy4PHlOBoO8ja51P8J+AoqKistb6qfl9/fXXnj/9oftJix+Ke+65Bx778ssvVR3Z8eSA4Bz5yw4hhBBC3IaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojTWDsoi4jI6tWrPTvaJiYmwvaoxLx79+6qjrYHF8GlbYUKFYJ9wkEr1Q22LAjkm2++UfUffvhB1VF5uUh4W8YnJCT4ah8ZGenRKlSo4Pt9165dq+pWmWrVqlVV/cSJE7BP8OcVExMDtxMX0bdf//TTT2F7VNaPbA7effddGAuVvaKSdBF9N9jk5GQZMmQI7BMMKi8XEVmzZo2qoxLzTp06wViFCxdWdVSSLiLSq1cveAwRERHhud/LlSsH2990002qjsqpX3/9dRgL2Xeg+1nk6nPRD0ePHvXsCG/tmFu+fHlV//HHH1Xd2qriWkm8B+u+1Xa7jYiI8PXssXbHRzucI4uJokWLwlhTpkxRdZS3iG7nEqrMWStXX758OWyPvqfQ9weyZhHB1hfWth/WM1ND+y5Cz5Jw2LVrFzyGnqPt27fPtffnLzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQpwlZjVWsWDGP+dw1MzFfoKorZBRpEWxWFshPP/3k0UJV82igagERbI6GjAu7dOkCY7Vr107V33nnHdjHrwnjmjVr5OLFi9m0evXqwfbIaHX37t2qblUEzJw5U9WtzyS4KiIqyh6m48aNk9OnT2fTbr/9dth+0aJFqo4+V8vwrk+fPqo+bdo02Oe3RjN+FcHXfNSoUTDWNWNED6+88grso1UfRkVFyfXXXw/7zJw502N2uG/fPtgeXZN58+apulVxtnLlSlUvU6YM7OOXmJgYzzMl+J4MBFVdoTGKKnxERFq3bq3qmZmZsM/f/vY3j1awYEF57LHHYB+tPWL69Omqjqr8WrRokeP3zQKZqYro1ZLx8fFSrVo1X+/RoEED38fQ83LMmDEw1s0336zqfr/XLFauXOmpvN68eTNsf/LkSVVHz5kdO3bAWL1791Z1qxpLq2qNjIyUkiVLqu35yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUJWY61bt85TZWT5sPjlnnvugcfQSmzLs6Zr166/+pxEcGWViMixY8dUPT4+XtVnzZoFYx0+fFjVrWoivxQoUMDjw2P5xqAKnJ9//lnVS5QoAWMNHz48B2eYneAqlVDVWEOHDvUVX/PFERE5deqUqmveW6H6/NYsXboUHkOeR8gvzKqwQfdn8+bNYR+r6goxcOBAj/bWW2/B9t9++62q79y5U9U///xzGAtVj0yaNAn2+dOf/gSPaSQnJ3s0VM1i8dVXX6n6HXfcAfugqraMjAzYp27duh4tNjYWtn///ffl7Nmz2TSrQgyNxf79+6u69QzVzlUEe/mJiHTs2BEeQ2RkZHi++1CFqgi+R8ePH6/qMTExMNahQ4dUfcOGDbBPsLdcRESE6Wupfec0btwYtke5o2re4KruQAoUKKDqVjUY8sdD8JcdQgghhDgNJzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQpwlZet6qVSuPtn//fti+aNGiqv7AAw+o+scffwxj9ejRQ9Vz0/xM5Gp5W3Bpds2aNWF7VP6JDFJTUlJgrNq1a6u6H8O9UOzZs8dTZnr//ffD9gsXLlT1Zs2aqfrbb78NY3Xr1k3Vx44dC/tUqVIFHssNqlev7qs9KvsUsUtPEZqJZlJSkgwYMCDHMdLT0+ExzYhTBG83oBnqZfH999+rulUKjIxIIyMjYR9tO4v8+fPD9qi8ddmyZar+3HPPwVjFixdXdau8fMmSJdle58+fX+rXrw/bHzlyxPO5hNpSQeP48eOqPnjwYNgHbWNhGZ1+8MEHvs5LK+W2thX55JNPVH3ixImqXqhQIRjr1VdfVXU0DsNlw4YNHqNM6zNEZs7IrNYyHO7evbuq+71OfpkyZQo81rRpU1+xtm7dCo+NHj1a1dE2GiL6FiL58uWTYsWKqe35yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUKWA2gVFMGVS4EEmzhmgYzfrKqcP/7xj6puVceEw/z58+X06dPZtBEjRsD2HTp0UPXU1FRVRxUtIthc87PPPoN9Bg0aBI9pXHfddZ7rcuTIEdgeVV0hkJmpiMiwYcNUPV++3JtnL1iwwFNtZpl3ooqdYOO8LG644QYYa8WKFar+0ksvwT5a9Q8ywhO5+vkGV5aULVsWtkfVCGjc3HnnnTBWjRo14DGEVXWFWLhwoecaWma1yKh33bp1MD7i9ddfV3Vk+CtiV4loaGa58+fPh+2RGS8au5mZmTAWMqS0Kpz8olXOVapUyXecuLg4VbcqgCdMmOD7fTST0JiYGNNc0q85c0JCgqqjXB599FEY680331T1OXPmwD6oAtoPWjV2Fqj6eNu2bapuGcMic1RUfSiimwcXK1ZMJk+erLbnLzuEEEIIcRpOdgghhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQp+FkhxBCCCFO49+JTkSqVq0Kjx09elTVGzdurOozZ86EsRYtWqTqV65cgX20ctW4uDjTtGzIkCEezTJ43Lx5s6qjcuCPPvoIxkJlv1Z5ebDxZoECBVQjviy0csodO3bA9siIExnVWYaG6Lysz1czhbSwDAc1GjVqpOqo9NPKD5XwI3PJ3OLs2bPwGCp5Rfj9/ETsa2QZGiIaNmzoiWmVUyPz0jfeeEPVLcNGa5uC3CIlJUUuXbqUTbv33nthe7SNxZYtW1S9Tp06MNaXX36p6jNmzIB9Vq9e7dFiYmLgVgTadiTR0dEwPkIzdxTB5fMiuEzfIpxrvmLFCo8RqFVe//DDD6t6ly5dVH3nzp0wFirnjo+Ph338smvXLs91jI2N9R3n5ZdfVvXk5GTYB5XJp6WlwT5+TVD5yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jTWAmX/BjcGpUqVUnVrMSVaHGV572jeKgFxgjvCQNaiVOTfghZOI88lEd0zJxTBPkoBi9RyJT+0mBMtPE1KSvIdK9jrKYfkOD+L66+/XtULFiyo6iVLloSxctPj6xqRwf/WxrvmRRQuyOMmt9/nGuo11MaWtfgyMTFR1dG9Zl3DXEbNz69fGHouomtlLYhHnwl6jolcXYwcTMCCY88YzS2QX5c1Ri1fuTBRr6H2mVjXFY1fdD3C+c4JZwGxgPy097fOCVGkSBFVt74nUH7aZ55DPBcmwqiqaCQi2MEyb9JYRAKd9FzLkfnlfQJzdD0/EfdydD0/EY7RvI7r+Yl4czQnO/lFpK6IpIpIWP8N/w8iUkRKicgqEQmsHXQlR+aXt/MT0XN0PT8Rd3J0PT8RjtG8nqPr+YngHM3JDiGEEEJInocLlAkhhBDiNNbqo/8LP225kiPzy9v5ifBPBHk9R9fzE+EYzes5up6fiPFnLGuyU1fcX7TkWo7ML+8TmKPr+Ym4l6Pr+YlwjOZ1XM9PRFmgbE12dHMWwd5QItjD47nnnlN1y/ti79698FiYBOeUKiKydu1auXjxYrYDpUuXhkGQP82TTz6p6i+++CKMddttt6n6sWPHYJ/gcsfo6OgsPys1Pw3Lh6VZs2aqXrt2bVW3fJqOHz+u6mPHjoV97r//fnRIzU8r+T906BCMj7yxvvrqK1Vfvnw5jHXzzTerev369WGfEKSCf2fj/PnzMMDkyZNVHZ3ruHHjYKzPPvtM1a2S17lz53q0uLi4rHGlXsPg+09EZMGCBfA9kI/Zjz/+qOpt2rSBsZ544glV79atG+xjoOY3ffp0z7NuyZIlMEiDBg1U/dtvv1V1y3eoZ8+eqm59Jm+++aZHK1CggHTt2lUkh2N0/vz5MP6kSZNU/e6771b1zp07w1iaL5fIVa8nxMmTJz1afHy8NG/eXMTHc9Ri/Pjxql6xYkVVnz59Ooy1Zs0aVV+8eDHsU758eXQoV/JD12TlypWqbm0lgbwz0bMsB3hysiY78OcsNLhERM6dO6fqBw4cUPXTp08bp5DrBOd0WeTqgzbY4C3YtC+QjIwMVd+/f7+qW19MaL8Z7eGfhbG3g5qfhnUN9+3bp+porxJrwoqMMtE4CUGO87P28UH5oc/Eys8yqwyTy+Df2bAKC9A9hcahNTEMp4DBGu/i4xpacdA1RNc9JSUFxkpPT4fHwkDNLy0tTc6cOZPtwOHDh2EQdA3RtbLGYTj3mjXmJYdjFD0nRXDuwZ/Rv9/EuJ/Rs/pXfCY5HqMWKBf03tZ4QOPd+p4yyJX80Pmic7X21LP+cx8mnpy4QJkQQgghTsPJDiGEEEKchpMdQgghhDhNSOOLpUuXev72+dJLL8H2yLMG8d1338Fj1apVU3Vj4ZV88803vt5f5OoC2+C/L1sL/rZu3arq6O/cXbp08R2rTp06sE9u8M477/jug3yu0KJCEZG2bduqOvKhCodRo0bJiRMnsmnW378Rd955p6qHs67M+hv06tWrPVpsbKw0adIkx/FnzZoFjz3//POqjq6T9b5orcu1BfEqDRs29GihvKE0D5wdO3bA9miBNPJQ6tGjB4yFFsv2798f9glei5YvXz4pVqwYbN+3b1/P+qff//73sL31jPMLWv/XunVr2AcVW/gB3fsiIgMHDlT11157TdVbtWoFY916662qbi2ItbzEENOnT/cUY1jehshLsHv37qq+cOFCGGvw4MGqbj3HrSKQnLJs2TJ47Pvv9QKuIUOGqPq9994LY6HF5GgdrIi+xjIqKgp6j/GXHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojTcLJDCCGEEKcJWXpeq1Ytj/dQ7969YfuHHnpI1ZFnVpEiRWCspk2bqrpV4hkO6H0QqCwd+XhY3lioBNMqQ/RLWlqa5xpavjiVK1dWdbQ1ueWzhSwYrNLs4LESFxdnli326tXL8z5vvfUWbI9AY1cri86iatWqql60aFHY55r/To7561//6il/R+XlIiLvvfeeqqNyfKtEFY0FC82rDJXhZrFmzRqPZUu/fv1g+woVKqg68o6ynlmVKlVSdeQLJmKXVWukp6d7LA9+/vlnXzEsLFsPNH6XLl0K+1il3hraNbc885BlwieffKLq1lYcaPsSa0uMcOjTp4+v9lOnTlV19Lmg8nIR7BdoPRdnzJiR7XVCQoJ07NgRtt+3b5/nGR+8pUcgyD4IPdutMbV7925VL1u2LOzjF/6yQwghhBCn4WSHEEIIIU7DyQ4hhBBCnIaTHUIIIYQ4DSc7hBBCCHGakNVYx44d86zQRivpLVDVyrx582Cf4OqMLKxKlE8//dSjxcfHm6vWd+zY4anmOXnyJGzfqFEjVZ8+fbqqI2M0EWxcuGrVKtinbt268JhGXFycR5s2bRps/9///d+qjlbmHz9+HMZCBm+zZ8+GffxSsWJFj2Z9fqiS5tSpU6o+c+ZMGOvDDz9Udese0araIiIiJCkpSW1foEABtdoFgap86tevr+o33XQTjHXgwAFVX7x4MezTokULj5Yvn/3/qvj4eImOjs6mWWanqHoD3YNW5dP777+v6g0aNIB9/JKWluZ5xiQkJMD2hQoVUvVwDHwfeOABVbeqsbTndVRUFDQo1a6vZfaLDDSDK4iysK4FqqazqsG0Z6LI1Rz9cObMGXjshx9+UHVkMIsMQkVEOnTooOponIjg7ylEsWLFPFV9f/jDH2B7ZJyMPttOnTrBWNozXETk4MGDsE96erpHi4qKgrH4yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaUIuPddWuq9btw62R1VXqLKiS5cuMFbLli1VvXTp0rDPsGHDPFooX54qVaqYx4PZunWrqjdp0kTVf/rpJxircOHCqm5VK/mtxgquchGx/ZmeeeYZVUdVD0OHDoWxrEqt3ELz/rGqCHr16qXqhw4dUvVvvvkGxgr2O8rCqrSZOHGiR0tMTJSePXuq7TWPKKsKBFWVvf3226pu+YgNGjRI1SdMmODr/UNVY1WrVs2jWVVi6B586qmnVL1mzZowVkpKinluGsGVopGRkeZzKSEhwVOFZ3nyoWuI7tuNGzfCWIsWLVJ16/MNxxMtGKsicfv27aq+fv16Vbe8sVCFmOUXplVrxsTEmONkzZo1cvHiRY+GCPazC8WIESPgserVq6s68oIT8XoyFi5cWP785z/D9pMmTfKcMxo7IiL79+9XdeRnhSpzRfTKKhHbB9O63zT4yw4hhBBCnIaTHUIIIYQ4DSc7hBBCCHEaTnYIIYQQ4jSc7BBCCCHEaTjZIYQQQojT+HM9u8ayZcvgMVRSeMstt6j66tWrfb//mDFj4LHIyEjf8TSssskvv/xS1bdt26bqd999N4yFjO8ee+wx2Ce4pDAcgksoA0EGfqh08IMPPoCxkFncwoULYR/r89LQSkyR+aEF2gbAKptG493aOkArH/ZrQIhKNUVwiTkqq127di2M9cgjj6j6XXfdBftY5ap+sD53ZATaunVrVb/xxhthrJdeeknVX3vtNdjHKtvW0Ax/P/roI9gePS+RGa+1fcBtt92m6qicWUR/lkVFRcHtJzZs2OB5pljl4mg7DlR6HmyiGggao2iLCRGRv/3tbx4t1PYItWvX9mjJycmw/aZNm1QdlcofO3YMxnr33XdVHW1XISJSsmTJbK+1LUgCadSokWdLBWRmKiLSsGFDVUfbcaCxI4K3oJk7dy7s0759e3hMg7/sEEIIIcRpONkhhBBCiNNwskMIIYQQp+FkhxBCCCFOw8kOIYQQQpwmrGqs+Ph4331QNYRmAJgFWh2fWxVXWRw8eNCzgvzKlSuwfa1atVS9b9++qm5VT6EV7eGYEyJ27NjhqWbo0aOH7ziWKRvi+eefV3VkGCsiMm/evGyv4+LioMmqiG70iowURUQGDx6s6qiKyeLZZ5/13Sc3WL58OTymGYeKiCxZssT3+0yaNEnVp06dCvv8/PPPHi0mJsas/tF477334LFp06apeps2bVQ9Li4Oxjp//ryv8xIR2bNnT7bXUVFRcv3118P227Zt89yDnTt3hu1RdUrXrl1VPTMzE8YqV66cqnfo0AH20UxxreduUlKSx+jUqi7SjDhFRBo3bqzqVnUqMsO0rnmhQoXgMT+MHDkSHpszZ46qowrcgwcPwljW8xLh936bM2eOp9qvbdu2sP3LL7+s6mXKlFF1dM1FRP7+97+rumXm6hf+skMIIYQQp+FkhxBCCCFOw8kOIYQQQpyGkx1CCCGEOA0nO4QQQghxGk52CCGEEOI0IUvPlyxZ4ilrRGZ7IrgsXSsPFhEZPXo0jIXKli1WrFjh0WJiYlQTtyxQqRwCGbmlpqaqumV62a1bN1VHpo0iIvv27cv2OjIyUjUazKJKlSoe7emnn4btly5dCo9pvPHGG77ah6JFixa/OoaVAyoxL1q0qKpbRpkZGRmqbpW9PvPMMx4tOTlZhg8fDvsEY43ZKVOmqPrYsWNVHd2bIriU2ypJPXLkiEcLZUJ45MgRz/YPZ8+ehe0XL16s6sgk2G8ZbiiCS5dDmUhaW2xonDlzRtWRSe+IESNgrHC2jChdurSv9lp5+969e2H7YcOGqTr6nLTtDLJA+Wnl878GrQzaMvxFZsSvvvqqqk+YMAHG2rFjh6rXq1cP9gk2W42JiYEGsyJXr2HwuEYmsiLYjPjBBx9U9a1bt8JYaLzv3LkT9jl8+LBHy58/v9StW1dtz192CCGEEOI0nOwQQgghxGk42SGEEEKI03CyQwghhBCnsRYoR4pcXfATjKZlgRbQIX+W5ORk4xT8ExMTY2nB5i65arKFcixSpIjvPtYCwWCPmoDXOc7P8oYpWbKkqqNzTUxMhLGiosKyX0PkOL+EhAQYBOVRuHBh/U0NTyBrcS9CG/NJSUn/frvAt0YxrHsQ4ffeFBEpXry4qlsLcrXFyAHjQL2GWjxrXKFzRjmG4+dnEXy+AeMgV54xaFyF8xwNGFu5RY7GqHXvly1bVtVLlSql6tYYRc9XVDyQA3LlGqKF08iLLTY2FsaynmeI4O/CgPtSzU+736xnHzondK2s8YCKQ6w+2jPQ+K6XCMNoq5GIfA/fKW/SWESWBbx2LUfml/cJzNH1/ETcy9H1/EQ4RvM6rucn4s3RnOzkF5G6IpIqIpdRozxCpIiUEpFVInIhQHclR+aXt/MT0XN0PT8Rd3J0PT8RjtG8nqPr+YngHM3JDiGEEEJInocLlAkhhBDiNJzsEEIIIcRpONkhhBBCiNNwskMIIYQQp/l/fHNFLVqJczMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过肉眼观察，可以很清楚地看到图像是带噪音的，也包含错误的像素。用噪音数据训练一个 PCA，要求投影后保存 50% 的方差："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.50).fit(noisy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里 50% 的方差对应 12 个主成份。现在来计算出这些成分，然后利用逆变换重构过滤后的手写数字:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(noisy)\n",
    "filtered_data = pca.inverse_transform(components)\n",
    "plot_digits(filtered_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 5.9.3特征脸   \n",
    "（无法下载数据集）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 5.9.4PCA总结  \n",
    "这一节讨论了用主成分分析进行降维、高维数据的可视化、噪音过滤，以及高维数据的特征选择。由于 PCA 用途广泛、可解释性强，所以可以有效应用于大量情景和学科中。对于任意高维的数据集，我倾向于以 PCA 分析开始，可视化点间的关系（正如手写数字示例中的处理方式），理解数据中的主要方差（正如特征脸示例中的处理方式），理解固有的维度（通过画出解释方差比）。当然，PCA 并不是一个对每个高维数据集都有效的算法，但是它提供了一条直接且有效的路径，来获得对高维数据的洞察。  \n",
    "  \n",
    "经常受数据集的异常点影响是 PCA 的主要弱点。因为这个理由，很多效果更好的 PCA 变体被开发出来，这些 PCA 变体方法迭代执行，丢弃对原始成分描述得很糟糕的数据点。Scikit-Learn 中有一些有趣的 PCA 变体，包括 RandomizedPCA 和 SparsePCA ，这两个算法也在 sklearn.decomposition 子模块中。我们刚才看到的 RandomizedPCA 算法使用了一个非确定方法，快速地近似计算出一个维度非常高的数据的前几个主成分，而 SparsePCA 引入了一个正则项（详情请参见 5.6 节）来保证成分的稀疏性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
